The theory to associate generalized matrix model with a class of algebra with an arbitrary logic can be found in [1]}. Indeed, if \(\langle A, {\cal C}\rangle \)  is a generalized matrix, then its Tarski congruence \( \widetilde{\bf \Omega }_{\bf A} F\)  is the largest congruence of \(\bf A\)  that is compatible with all members of \(\cal C\) ; it is not hard to show that:
\( \widetilde{\bf \Omega }_{\bf A} F=\bigcap \limits _{F\in \cal C} {\bf \Omega _A} F\) 
